Greatest Common Factor
• Factors of a number are any numbers which divide into a given number
evenly.
Factors of 24: 1, 2, 3, 4, 6, 8, 12, 24
Factors of 36: 1, 2, 3, 4, 6, 9, 12, 18, 36
• Common factors are 1, 2, 3, 4, 6, & 12. The largest of these (12) is the
greatest common factor (GCF).
• Listing factors is one way to find the GCF.
• A second method uses prime factorizations of each number using a Factor
Tree.
• To find the GCF, factor each number into its prime factors.
• Select each factor which occurs in every set of factors.
Example:
24
36
4·6
4·9
2·2·2·3
2·2·3·3
Matching Factors are:
2 · 2 · 3 12
• The Greatest Common Factor will always be less than or equal to the
smallest given number.
Example: Find the GCF of 48, 72, and 24.
48
72
24
8·6
8·9
4·6
2·4·2·3
2·4·3·3
2·2·2·3
2·2·2·2·3
2·2·2·3·3
GCF: 2 · 2 · 2 · 3 24
Arrows indicate “Divides Into”:
LCM
Number
Number
GCF